Hyperbrane Relativity: Brane Thickness as Universal Crossover Scale Unifying Force-Law and Quantum-Measurement Regimes (HBR Complete Master Edition V28)

Hyperbrane Relativity (HBR) describes the observable universe as a dynamical 3-brane uniformly translating in the -W direction within a flat 4D Euclidean bulk. The empirical 3D light speed c is identified with the gate-inflow speed at the dimensional boundary Sigma = {w = w_brane(t)} via a Dirichlet-type condition (dot X^W |_Sigma = c); E = mc^2 then arises as a geometric identity from the self-contraction |U_inflow|^2 = c^2. Lorentz invariance is treated as an emergent brane symmetry, not a fundamental postulate. The framework yields a single-parameter modification beta of general relativity through the field equation G_munu + beta H_munu = 8 pi T_munu, with weak-field expansion Phi = 1 + Phi_N/c^2 + beta Phi_N^2/c^4 and PPN metric g_00 = -1 + 2U - 2 beta U^2. Key observational results carried over from prior versions: PPN constraint |beta - 1| < 10^-4 (Cassini), SPARC 171-galaxy MCMC fit with chi^2_nu = 1.29 (V26), and falsifiable predictions including a sub-leading 1/r^3 phase correction detectable by Einstein Telescope / Cosmic Explorer at SNR > 30. V28 introduces the central new theoretical contribution (Core Novelty 9): the brane thickness Delta-w is identified as the universal crossover scale that simultaneously controls (i) the strong-field force-law transition between the near-field 1/r^4 singularity-avoidance regime (r <~ Delta-w) and the far-field 1/r^3 correction to Newtonian gravity (r >> Delta-w), and (ii) the Observation-Contact Separation underlying quantum measurement, with the contact regime |Delta-kappa| L <~ 1 corresponding to L ~ Delta-w for any compact apparatus. Both crossovers are dual expressions of a single geometric fact: two HBR objects' W-axis helical threads overlap if and only if their separation is less than Delta-w. HBR is therefore a one-scale theory with cross-regime falsifiability that has no analogue in either General Relativity or the Standard Model. This unification is presented in Part I, Section 'The Fundamental Scale: Brane Thickness Delta-w as Universal Crossover Geometry', with reinforcement at the start of Appendix B. V28 also performs comprehensive ontological reconciliation across all parts: the static-brane (V24) and uniform-translation (V25-V27) descriptions are unified by treating brane translation as the kinematic origin of the gate inflow at speed c. V27 ontological notes are added at the head of Parts XI, XIII, XIV, XV, and XVI to make explicit that all derived results survive the V27 framing. All forbidden language ('drift', 'static brane', SF-style phrasing) has been purged from the manuscript and figures. V28 retains the V27 appendices: (A) Gleason-type structural origin of the Born rule via measure uniqueness on kappa-space, deriving the quadratic probability measure through a Cauchy functional equation; and (B) rigorous OCS formulation via harmonic analysis with three-regime classification: contact (|Delta-kappa| L << 1), transition (|Delta-kappa| L ~ 1), and observation (|Delta-kappa| L >> 1). Appendix B now opens by referencing the Delta-w unification, making explicit that the Born rule derivation and OCS theorem are not independent results but consequences of a single geometric scale. Released under CC-BY-4.0. PDF includes both English and Japanese editions.